A353512 n multiplied by the least nonzero digit missing from its primorial base representation.

0, 2, 4, 6, 4, 15, 12, 14, 16, 18, 30, 33, 12, 39, 42, 45, 16, 51, 18, 38, 40, 42, 22, 92, 24, 50, 52, 54, 28, 87, 60, 62, 64, 66, 102, 105, 72, 74, 76, 78, 120, 123, 126, 129, 132, 135, 138, 141, 96, 98, 100, 102, 208, 212, 108, 110, 112, 114, 174, 177, 60, 183, 186, 189, 64, 195, 198, 201, 204, 207, 210, 213, 72

Offset

0,2

Links

Amiram Eldar, Table of n, a(n) for n = 0..10000

Index entries for sequences related to primorial base.

Formula

a(n) = n * A329028(n).

Example

19 in primorial base (A049345) is written as "301". The least missing nonzero digit is 2, thus A329028(19) = 2 and a(19) = 2*19 = 38.

Mathematica

a[n_] := Module[{k = n, p = 2, s = {}, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, AppendTo[s, r]; p = NextPrime[p]]; n * Min[Complement[Range[Max[s]+1], s]]]; a[0] = 0; Array[a, 100, 0] (* Amiram Eldar, Mar 13 2024 *)

Prog

(PARI)
A329028(n) = { my(m=Map(), p=2); while(n, mapput(m, (n%p), 1); n = n\p; p = nextprime(1+p)); for(k=1, oo, if(!mapisdefined(m, k), return(k))); };
A353512(n) = (n * A329028(n));

Crossrefs

Cf. A049345, A328840 (the fixed points, positions where a(n) = n), A329028.

Cf. also A257080 for analogous sequence.

Sequence in context: A371241 A278259 A293473 * A257080 A099784 A365160

Adjacent sequences: A353509 A353510 A353511 * A353513 A353514 A353515

Keyword

nonn,base

Author

Antti Karttunen, Apr 27 2022

Status

approved